The 26-year-old joined the Rossoneri from Marseille in the summer but has struggled for a regular first-team berth.
Taiwo, who can also operate in midfield, had been linked with a January move to injury-plagued Arsenal but has now joined QPR after securing a work permit, becoming Mark Hughes' first signing.
"It's a new and exciting challenge for me and one I am very much looking forward to," the Nigeria international told the club's official website, www.qpr.co.uk.
"I'm very grateful to Mark Hughes for bringing me here. It is always nice for a player when you know the manager wants you and I will repay his faith in me.
"I can't wait to play for the club. I know only hard work, good performance, dedication, and passion will connect me with the fans but I'm prepared.
"I'm looking forward to what lies ahead and I'm prepared to give my all to the QPR cause."
The news will come as a relief to QPR, having seen moves for Brazilian duo Henrique and Alex fall through over the past 24 hours.
The former looked set for a move to Loftus Road until work permit problems halted the deal, while Press Association Sport understands Chelsea centre-back Alex will not be joining the Rs after failing to agree personal terms.
QPR are still hoping to tie a deal up for Manchester City defender Nedum Onuoha but, in the meantime, Hughes is relieved to complete the signing of Taiwo.
"I have known of him for a long time and admired him from afar," the QPR boss said.
"To get him now is a fantastic coup and a real statement of intent that we can attract the quality of player that he is. I am looking forward to working with him.
"He has got great ability, a good reputation in the game and a great personality.
"He plays with a smile on his face and I think QPR fans are going to enjoy seeing him play for us."